Spatial-Temporal Modeling and Computation for Physical Processes and Numerical Simulations

每一天的每一分钟，都有一群卫星捕捉到下面场景的图像，超级计算机大量模拟未来的天气和气候，积累了大量关于地球及其大气的原始信息。由于大量公共资金已用于收集和制作这类数据，统计工具必须能够胜任分析这些数据的任务。这个项目的目的是整理这些信息，准确地填补原始数据中的空白，从一系列图像中推断有意义的量--例如变化的风型--并通过计算机数值模拟的分析来提炼我们对地球作为一个相互关联的系统的理解。在该项目期间开发的统计技术将通过向公众传播软件向更广泛的社区提供。学生和新兴研究人员将接受使用新方法的培训，并将获得专门知识和独立批判性思维技能，以冒险并产生自己的影响。该项目概述了地球科学数据分析管道中三项关键任务的进展。(1)地面监测仪和极地轨道卫星的观测结果往往在空间和时间上存在差距，必须进行内插。因此，提出了新的高斯过程近似，它在改进近似的同时显著地减少了计算量，从而允许快速和准确的内插。(2)地球同步卫星传感器提供了对大气进行精细、持续监测的机会。这项建议概述了一个框架，用于利用这些数据--包括图像的时间序列--来推断高空风场。(3)超级计算的速度继续提高了我们产生高分辨率数值模拟的能力，这需要新的计算工具来分析输出。提出了一种用于局部评估的技术，从而产生一个全球有效的统计模型，这是一个关键特征，能够通过统计模型进行数值模型仿真和数据压缩。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Every minute of every day, a swarm of satellites captures images of the scenes below, and supercomputers churn out simulations of future weather and climate, accumulating a mountain of raw information about the Earth and its atmosphere. Since a significant amount of public funding has been devoted to the collection and production of this data, it is imperative that statistical tools be up to the task of analyzing it. This project aims to sort through this information, accurately filling in gaps in the raw data, inferring meaningful quantities--such as changing wind patterns--from sequences of images, and refining our understanding of the Earth as an interconnected system through the analysis of numerical computer simulations. Statistical techniques developed during this project will be made accessible to the broader community by public dissemination of software. Students and emerging researchers will be trained to use the new methods and will be empowered with specific knowledge and independent critical thinking skills to venture out and make their own impacts.The project outlines advancements for three crucial tasks in the geoscientific data analysis pipeline. (1) Observations from ground monitors and polar orbiting satellites often have gaps in space and time that must be interpolated. Thus, new Gaussian process approximations are proposed that significantly reduce computational effort while improving approximations, allowing for fast and accurate interpolations. (2) Geostationary satellite sensors afford the opportunity for fine scale, continual monitoring of the atmosphere. This proposal outlines a framework for using these data--which consist of a temporal sequence of images--for the purpose of inferring upper air wind fields. (3) The pace of supercomputing has continued to increase our ability to produce high-resolution numerical simulations, which requires new computational tools for analyzing the output. A technique is proposed for local estimation that results in a globally valid statistical model, a critical feature that enables numerical model emulation and data compression via statistical models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.